Of the cars in a used-car lot, 2/5 are the color gray. 1/3 of the gray cars are electrically powered vehicles. What fraction of the cars on the lot are both gray and electrically powered? Leave your answer in simplified fraction form.(1 point)

Answer 1

To find the fraction of the cars on the lot that are both gray and electrically powered, we can follow these steps:

1. Let the total number of cars in the lot be represented as \( C \).

2. The fraction of gray cars is given as \( \frac{2}{5} \). Therefore, the number of gray cars is:

   \[ \text{Number of gray cars} = \frac{2}{5} C \]

3. It’s given that \( \frac{1}{3} \) of the gray cars are electrically powered. Thus, the number of electrically powered gray cars is:

   \[ \text{Number of electrically powered gray cars} = \frac{1}{3} \times \frac{2}{5}C = \frac{2}{15}C \]

4. Finally, to find the fraction of the total cars that are both gray and electrically powered, we take the number of electrically powered gray cars and divide it by the total number of cars \( C \):

   \[ \text{Fraction of cars that are gray and electrically powered} = \frac{\frac{2}{15}C}{C} = \frac{2}{15} \]

Thus, the fraction of the cars on the lot that are both gray and electrically powered is \( \frac{2}{15} \).